@tec Your programming skills are FAR beyond what I can do. I started exploring voting options about 7 months ago, and seeing that IRV sometimes selects an outcome that is clearly not the best choice, it occurred to me that looking at the second choice of the ballots of the runner up made sense. That led to a sort of double-elimination approach. Using a spreadsheet to lay out a few scenarios, it appeared that the approach had some promise. Unable to find anyone to help me, I managed to create some php webpages that can be used to evaluate scenarios. Testing with that I found some anomalies so progressed to a hybrid approach. So far, it's checking out just fine.

I like the visual layout that you provided, and I haven't seen anything with the "indifference lines". It's similar to this: https://ncase.me/ballot/, which you're probably familiar with. I'd like to be able to start with ballot numbers and then have them displayed, rather than being limited to manipulating the image (which I think is fantastic too).

I was wondering too if your program calculates the distance between the two other options and then sets the second choice as the closest one.

Here's a link to the crude pages that I put together: https://wethepeople.ca/WTP_IRV-DEp1tester.php

I would definitely like to collaborate with you on an "evaluation framework".

Here is another good article

https://psephomancy.medium.com/a-majority-of-voters-1d990a53b089

@brozai I see, yes according to what I've learned about it QV tends to incorporate the strengths of interests and not just the proportion of people with those interests. Depending on what is desired that may be a good thing or a bad thing. There has also been research on its resistance to collusion and it seems to hold up very well, which is a property that I definitely like.

I found this presentation very interesting:

Youtube Video

One point brought up by an audience member during the Q&A was that QV seems to illuminate the relative preferences of the electorate, which show up in the presenter's data as approximate Gaussian distributions and the grouping together of different strata of right-wing and left-wing groups, which does not occur without the quadratic cost.

@marylander Thanks yup, this looks like a counterexample.

Using some of the ideas in your construction I found a slightly smaller one on 8 nodes

cd7a0a63-764a-466c-ab71-8fa9552bf2fb-image.png

Okay, so in my recent reading, I found a different result which sounds a lot more like the one I was hunting for here. The theorem is called the McKelvey–Schofield chaos theorem, the reference paper appears to be Intransitivities in multidimensional voting models and some implications for agenda control.

Anyway, for the statement of the theorem, I'll quote the Handbook of Social Choice and Welfare (Chap. 13, p.27):

Richard McKelvey has stated a famous theorem: Suppose the alternatives lie in an n-dimensional space (n > 1), we choose between alternatives by majority voting (as is standard in legislation), and there is no Condorcet winner. Given any two proposals, a and b, there exists a sequence of proposals, {a'_i}(i = 0, ..., n) such that a'_0 = a, a'_n = b, and a'_i defeats a'_{i+1} for all i = 0, ..., n−1. That is, by a suitably chosen agenda, any proposal can defeat any other if there is no Condorcet winner.